| Multiple Linear Regression - Estimated Regression Equation |
| us/ch[t] = + 2.10935943686758 -0.734389206628538`eu/us`[t] + e[t] |
| Multiple Linear Regression - Ordinary Least Squares | |||||
| Variable | Parameter | S.D. | T-STAT H0: parameter = 0 | 2-tail p-value | 1-tail p-value |
| (Intercept) | 2.10935943686758 | 0.028181 | 74.851 | 0 | 0 |
| `eu/us` | -0.734389206628538 | 0.02018 | -36.3916 | 0 | 0 |
| Multiple Linear Regression - Regression Statistics | |
| Multiple R | 0.981284059913598 |
| R-squared | 0.962918406240514 |
| Adjusted R-squared | 0.962191316166798 |
| F-TEST (value) | 1324.34541613257 |
| F-TEST (DF numerator) | 1 |
| F-TEST (DF denominator) | 51 |
| p-value | 0 |
| Multiple Linear Regression - Residual Statistics | |
| Residual Standard Deviation | 0.0102367726314117 |
| Sum Squared Residuals | 0.00534436720926817 |
| Multiple Linear Regression - Actuals, Interpolation, and Residuals | |||
| Time or Index | Actuals | Interpolation Forecast | Residuals Prediction Error |
| 1 | 1.08 | 1.08855843965391 | -0.00855843965390507 |
| 2 | 1.12 | 1.12527789998534 | -0.00527789998533506 |
| 3 | 1.12 | 1.13262179205162 | -0.0126217920516204 |
| 4 | 1.16 | 1.15465346825048 | 0.0053465317495233 |
| 5 | 1.16 | 1.16934125238305 | -0.00934125238304747 |
| 6 | 1.16 | 1.16199736031676 | -0.00199736031676209 |
| 7 | 1.16 | 1.16199736031676 | -0.00199736031676209 |
| 8 | 1.15 | 1.16934125238305 | -0.0193412523830475 |
| 9 | 1.17 | 1.17668514444933 | -0.00668514444933285 |
| 10 | 1.16 | 1.18402903651562 | -0.0240290365156182 |
| 11 | 1.19 | 1.16199736031676 | 0.0280026396832379 |
| 12 | 1.13 | 1.11059011585276 | 0.0194098841472356 |
| 13 | 1.14 | 1.13262179205162 | 0.00737820794837943 |
| 14 | 1.13 | 1.11793400791905 | 0.0120659920809502 |
| 15 | 1.16 | 1.14730957618419 | 0.0126904238158087 |
| 16 | 1.17 | 1.15465346825048 | 0.0153465317495233 |
| 17 | 1.14 | 1.13996568411791 | 3.43158820940498e-05 |
| 18 | 1.14 | 1.13262179205162 | 0.00737820794837943 |
| 19 | 1.11 | 1.11059011585276 | -0.000590115852764216 |
| 20 | 1.12 | 1.11793400791905 | 0.00206599208095041 |
| 21 | 1.08 | 1.08121454758762 | -0.00121454758762287 |
| 22 | 1.07 | 1.07387065552134 | -0.0038706555213375 |
| 23 | 1.09 | 1.08121454758762 | 0.00878545241237714 |
| 24 | 1.08 | 1.08121454758762 | -0.00121454758762287 |
| 25 | 1.08 | 1.08121454758762 | -0.00121454758762287 |
| 26 | 1.08 | 1.07387065552134 | 0.00612934447866251 |
| 27 | 1.09 | 1.08121454758762 | 0.00878545241237714 |
| 28 | 1.08 | 1.08855843965391 | -0.00855843965390826 |
| 29 | 1.07 | 1.07387065552134 | -0.0038706555213375 |
| 30 | 1.07 | 1.06652676345505 | 0.00347323654494789 |
| 31 | 1.07 | 1.05918287138877 | 0.0108171286112333 |
| 32 | 1.08 | 1.06652676345505 | 0.0134732365449479 |
| 33 | 1.07 | 1.06652676345505 | 0.00347323654494789 |
| 34 | 1.06 | 1.05918287138877 | 0.000817128611233264 |
| 35 | 1.06 | 1.05918287138877 | 0.000817128611233264 |
| 36 | 1.06 | 1.05918287138877 | 0.000817128611233264 |
| 37 | 1.04 | 1.03715119518991 | 0.00284880481008939 |
| 38 | 1.03 | 1.02980730312363 | 0.000192696876374768 |
| 39 | 1.03 | 1.02980730312363 | 0.000192696876374768 |
| 40 | 1.04 | 1.03715119518991 | 0.00284880481008939 |
| 41 | 1.03 | 1.02980730312363 | 0.000192696876374768 |
| 42 | 1.02 | 1.01511951899105 | 0.00488048100894553 |
| 43 | 1.01 | 1.00777562692477 | 0.00222437307523091 |
| 44 | 1.03 | 1.02980730312363 | 0.000192696876374768 |
| 45 | 1.02 | 1.02246341105734 | -0.00246341105733985 |
| 46 | 1.01 | 1.01511951899105 | -0.00511951899105448 |
| 47 | 1.02 | 1.01511951899105 | 0.00488048100894553 |
| 48 | 1.01 | 1.00777562692477 | 0.00222437307523091 |
| 49 | 1.02 | 1.02246341105734 | -0.00246341105733985 |
| 50 | 1.03 | 1.03715119518991 | -0.00715119518991061 |
| 51 | 1.04 | 1.05918287138877 | -0.0191828713887668 |
| 52 | 1.04 | 1.05183897932248 | -0.0118389793224814 |
| 53 | 1.03 | 1.05918287138877 | -0.0291828713887668 |
| Goldfeld-Quandt test for Heteroskedasticity | |||
| p-values | Alternative Hypothesis | ||
| breakpoint index | greater | 2-sided | less |
| 5 | 0.347973323759285 | 0.695946647518571 | 0.652026676240715 |
| 6 | 0.201198821532569 | 0.402397643065139 | 0.798801178467431 |
| 7 | 0.106381748963203 | 0.212763497926405 | 0.893618251036797 |
| 8 | 0.309007678706755 | 0.61801535741351 | 0.690992321293245 |
| 9 | 0.218950188093510 | 0.437900376187021 | 0.78104981190649 |
| 10 | 0.594880177958573 | 0.810239644082854 | 0.405119822041427 |
| 11 | 0.992922958464653 | 0.0141540830706935 | 0.00707704153534675 |
| 12 | 0.998063560906294 | 0.00387287818741149 | 0.00193643909370575 |
| 13 | 0.996808719594157 | 0.00638256081168678 | 0.00319128040584339 |
| 14 | 0.99605468341386 | 0.0078906331722805 | 0.00394531658614025 |
| 15 | 0.996318816225984 | 0.00736236754803192 | 0.00368118377401596 |
| 16 | 0.99793493768338 | 0.00413012463323948 | 0.00206506231661974 |
| 17 | 0.996063830737429 | 0.00787233852514246 | 0.00393616926257123 |
| 18 | 0.994091015194252 | 0.0118179696114954 | 0.0059089848057477 |
| 19 | 0.990403450871431 | 0.0191930982571382 | 0.00959654912856912 |
| 20 | 0.98405027261104 | 0.0318994547779207 | 0.0159497273889604 |
| 21 | 0.977247873145573 | 0.0455042537088539 | 0.0227521268544269 |
| 22 | 0.96965693086991 | 0.0606861382601808 | 0.0303430691300904 |
| 23 | 0.96375457292605 | 0.0724908541479017 | 0.0362454270739508 |
| 24 | 0.946657909768944 | 0.106684180462112 | 0.0533420902310559 |
| 25 | 0.922879356545837 | 0.154241286908325 | 0.0771206434541626 |
| 26 | 0.902695972840033 | 0.194608054319934 | 0.097304027159967 |
| 27 | 0.901725406751018 | 0.196549186497963 | 0.0982745932489817 |
| 28 | 0.886688170591792 | 0.226623658816417 | 0.113311829408209 |
| 29 | 0.849914274717306 | 0.300171450565387 | 0.150085725282694 |
| 30 | 0.80974300336621 | 0.380513993267581 | 0.190256996633790 |
| 31 | 0.836149023535563 | 0.327701952928875 | 0.163850976464437 |
| 32 | 0.929558351718444 | 0.140883296563113 | 0.0704416482815563 |
| 33 | 0.942267822705711 | 0.115464354588578 | 0.0577321772942889 |
| 34 | 0.944782943096855 | 0.110434113806290 | 0.0552170569031448 |
| 35 | 0.960130636186654 | 0.079738727626693 | 0.0398693638133465 |
| 36 | 0.987420851004243 | 0.0251582979915147 | 0.0125791489957573 |
| 37 | 0.990944013382798 | 0.0181119732344032 | 0.00905598661720162 |
| 38 | 0.985887158957434 | 0.0282256820851320 | 0.0141128410425660 |
| 39 | 0.978734993339433 | 0.0425300133211332 | 0.0212650066605666 |
| 40 | 0.991576267476562 | 0.0168474650468756 | 0.0084237325234378 |
| 41 | 0.989515760825935 | 0.0209684783481307 | 0.0104842391740653 |
| 42 | 0.981989232867816 | 0.0360215342643676 | 0.0180107671321838 |
| 43 | 0.965251089421542 | 0.0694978211569151 | 0.0347489105784576 |
| 44 | 0.961838195896234 | 0.0763236082075321 | 0.0381618041037660 |
| 45 | 0.923041851172113 | 0.153916297655774 | 0.0769581488278869 |
| 46 | 0.914090629739952 | 0.171818740520096 | 0.085909370260048 |
| 47 | 0.848936088395094 | 0.302127823209811 | 0.151063911604906 |
| 48 | 0.746607166687555 | 0.50678566662489 | 0.253392833312445 |
| Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity | |||
| Description | # significant tests | % significant tests | OK/NOK |
| 1% type I error level | 6 | 0.136363636363636 | NOK |
| 5% type I error level | 18 | 0.409090909090909 | NOK |
| 10% type I error level | 23 | 0.522727272727273 | NOK |
